A train takes 2 hours less for a journey of 300km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train.
Answers
❤Here is your solutions ❤
Given :-
A train takes 2 hours less for a journey of
Distance is 300km if speed 5km/h from its usual speed.
Let x = usual speed
A/q
=>300 / (x + 5) + 2 = 300 / x
=>(310 + 2x) / (x + 5) = 300 / x
Now cross multiply
=>310x + 2x^2 = 300x + 1500
=>2x^2 + 10x - 1500 = 0
=>x^2 + 5x - 750 = 0
=>(x - 25) (x + 30) = 0
=>x = -30 or x = 25
x = 25 km /h
(distance measures in positive .)
Hence
The usual speed of the train is 25km/h
Hope it helps you.
HEY THERE!!!!
A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train.
Method of Solution;-
Let to be actual Speed of the train = x km/hr
•°• Given; -
Total Distance covered by train = 300 kilometers.
•°• Time Taken = 300/x. -----(1)
Now, According to the Question!!
Speed increase = x+5
•°• Speed = x+5/300. ---------(2)
From Equation (1) and (2)
300/x - 300/x+5 = 2
=> 300x + 1500-300x /x(x+5) = 2
=> 1500/x²+5x = 2
=> 1500 = 2x²+10x
•°• 2x²+10x -1500 = 0
=> 2(x²+5x-750) = 0
•°• x²+5x -750 = 0
=> x²+30x-25x -750 = 0
=> x(x+30) -25(x+30) = 0
•°• (x+30)(x-25)=0
Here, x-25 = 0
•°• x = 25, -30
Note:- Neglected (-30)
Hence, x = 25 km/hr
Conclusion;-
Actual Speed of the train = 25 km/hr